The inductance of a straight wire is usually so small that it is neglected in most practical problems. If the problem deals with very high frequencies (f > 20 GHz), the calculation may become necessary. For the rest of this book, we will assume that this self-inductance is negligible.

Inductance of a short air core cylindrical coil in terms of geometric parameters:Edit

There are several important properties for an inductor that may need to be considered when choosing one for use in an electronic circuit. The following are the basic properties of a coil inductor. Other factors may be important for other kinds of inductor, but these are outside the scope of this article.

Current carrying capacity is determined by wire thickness and resistivity.

The quality factor, or Q-factor, describes the energy loss in an inductor due to imperfection in the manufacturing.

The inductance of the coil is probably most important, as it is what makes the inductor useful. The inductance is the response of the inductor to a changing current.

The inductance is determined by several factors.

Coil shape: short and squat is best

Core material

The number of turns in the coil. These must be in the same direction, or they will cancel out, and you will have a resistor.

Coil diameter. The larger the diameter (core area) the larger the induction.

Permeability of the core is μ. μ is given by the permeability of free space, μ0 multiplied by a factor, the relative permeability, μr

The current in the coil is 'i'

The magnetic flux density, B, inside the coil is given by:

B=Nμil{\displaystyle B={\frac {N\mu i}{l}}}

We know that the flux linkage in the coil, λ, is given by;

λ=NBA{\displaystyle \lambda =NBA\,}

Thus,

λ=N2Aμli{\displaystyle \lambda ={\frac {N^{2}A\mu }{l}}i}

The flux linkage in an inductor is therefore proportional to the current, assuming that A, N, l and μ all stay constant. The constant of proportionality is given the name inductance (measured in Henries) and the symbol L:

We call −E{\displaystyle -{\mathcal {E}}} the electromotive force (emf) of the coil, and this is opposite to the voltage v across the inductor, giving:

v=Ldidt{\displaystyle v=L{\frac {di}{dt}}}

This means that the voltage across an inductor is equal to the rate of change of the current in the inductor multiplied by a factor, the inductance. note that for a constant current, the voltage is zero, and for an instantaneous change in current, the voltage is infinite (or rather, undefined). This applies only to ideal inductors which do not exist in the real world.

This equation implies that

The voltage across an inductor is proportional to the derivative of the current through the inductor.

In inductors, voltage leads current.

Inductors have a high resistance to high frequencies, and a low resistance to low frequencies. This property allows their use in filtering signals.

An inductor works by opposing current change. Whenever an electron is accelerated, some of the energy that goes into "pushing" that electron goes into the electron's kinetic energy, but much of that energy is stored in the magnetic field. Later when that or some other electron is decelerated (or accelerated the opposite direction), energy is pulled back out of the magnetic field.